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On Hyperbolic Equations with a Translation Operator in Lowest Derivatives

Author

Listed:
  • Vladimir Vasilyev

    (Center of Applied Mathematics, Belgorod State National Research University, Pobedy St. 85, Belgorod 308015, Russia)

  • Natalya Zaitseva

    (Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, GSP-1, Leninskie Gory, Moscow 119991, Russia)

Abstract

In the half-plane, a solution to a two-dimensional hyperbolic equation with a translation operator in the lowest derivative with respect to a spatial variable varying along the entire real axis is constructed in an explicit form. It is proven that the solutions obtained are classical if the real part of the symbol of a differential-difference operator in the equation is positive.

Suggested Citation

  • Vladimir Vasilyev & Natalya Zaitseva, 2024. "On Hyperbolic Equations with a Translation Operator in Lowest Derivatives," Mathematics, MDPI, vol. 12(12), pages 1-8, June.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:12:p:1896-:d:1417760
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    References listed on IDEAS

    as
    1. Vladimir Vasilyev & Natalya Zaitseva, 2023. "Classical Solutions of Hyperbolic Equation with Translation Operators in Free Terms," Mathematics, MDPI, vol. 11(14), pages 1-9, July.
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